AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 3

Scale Drawings: Compass Directions & Distance on a Grid

What this question tests

This question assesses your ability to:

Identify cardinal compass directions (North, South, East, West) from a reference arrow.
Read distances from a scale grid (counting grid squares accurately).
Use a given scale ratio ( 1 cm represents 10 m ) to convert diagram lengths to real-world actual distances.
Carefully interpret question phrasing, specifically calculating the total distance along a path rather than the direct straight-line displacement.

Question 3 (a) • 1 Mark

Direction of B from A

✅ Correct Answers

East (or E)
Due East or Easterly
090° (acceptable 3-figure bearing)

💡 Key Knowledge

Remember your standard compass points:

North points straight up (shown by the arrow).
Moving clockwise: North → East → South → West.
"Direction of B from A" means: imagine you are standing at A and looking towards B. You are looking directly to the right, which is East.

🧠 Exam Technique

Always circle the word "from". Many students look from B to A instead, which would give West. Starting at point A and moving to point B goes directly to the right (→), meaning East.

❌ Common Errors

Writing casual directions like "Right" or "Across" — these score 0 marks because mathematical direction requires compass points or bearings.
Writing a two-digit bearing like 90 instead of 090 (bearings require three figures).
Giving multiple conflicting answers, e.g. "East or North-East" (scored as choice, 0 marks).

Mark Scheme Breakdown:
• B1: East / E / Due East / Easterly / 090 (ignore any extra reference to distance).

Question 3 (b) • 2 Marks

Actual Distance Along the Path from A to C

📐 Step-by-Step Calculation

Count the grid units along each segment of the path:
From A to B = 4 grid squares = 4 cm
From B to C = 3 grid squares = 3 cm
Find the total length on the grid:
Total grid distance = 4 cm + 3 cm = 7 cm
Apply the scale (1 cm represents 10 metres):
Actual distance = 7 × 10 = 70 metres

Alternative valid method: Convert each leg first → (4 × 10) + (3 × 10) = 40 m + 30 m = 70 metres.

✅ Final Answer

70 metres

❌ Common Calculation Traps

Finding direct straight-line distance (50 m): Using Pythagoras (√(4² + 3²) = 5 cm → 50 m) measures "as the crow flies". The question specifically asked for distance along the path. (Awarded Special Case SC1).
Incomplete scaling: Scaling one side but not the other, e.g. (3 × 10) + 4 = 34 m (scores M1 A0).
Halving or further operations: Finding 70 then dividing by 2 to get 35 (scores M1 A0).

Mark Scheme Breakdown:
• M1 (Method): For showing 4 × 10 (or 40), or 3 × 10 (or 30), or adding grid squares 4 + 3 (or 7). May be written directly on the grid diagram.
• A1 (Accuracy): 70.
• Special Case: SC1 for an answer of 50 (calculating straight line from A to C).